The quickest detections of power quality (PQ) events have been a critical issues in smart grids due to the wide adoption of renewable energy sources and delicate power electronic devices. The Advanced Metering Infrastructure (AMI), which consists of multiple smart meters/sensors, is adopted to quickly detect the PQ events. In AMI network, multiple meters will send their local decisions to a data collecter/fusion center. The fusion center will make the final decision. The bandwidth between each meter to the fusion center is constrained to be only 1 bit for reducing the cost of communications. Moreover, some of the meters may be faulty in the considered AMI network. We propose a new one-bit randomized grouping algorithm to detect the PQ events with fault tolerant capability. Our simulation results show that our proposed algorithm can efficiently combat faulty meters, and have superior performance with previous works.